The Fractal Adaptive Moving Average or better known as FRAMA, is a technical indicator developed by John Ehlers. This indicator is constructed based on the algorithm of the Exponential Moving Average, in which the smoothing factor is calculated based on the current fractal dimension of the price series. The advantage of FRAMA is the possibility to follow strong trend movements and to sufficiently slow down at the moments of price consolidation.

## What is the Fractal Adaptive Moving Average?

According to John Ehlers, that market prices are fractal. Fractals are intricate patterns that create continuous shapes. Fractal shapes are almost similar. This means they have similar characteristics. This definition is based on a mathematical principle. John Ehlers stated that if a certain pattern is removed from charts like a 5-minute or a daily chart, a trader may find it difficult to separate them. This is the characteristic that makes markets fractal.

** **An Adaptive Moving Average (AMA) is one more moving average overlay, just like EMA. It changes its sensitivity to price fluctuations. The Adaptive Moving Average becomes more sensitive during periods when price is moving in a certain direction and becomes less sensitive to price movement when price is volatile.

### Fractal Moving Average calculation

The Fractal Adaptive Moving Average calculation is very complex and requires a certain set of elements for gauging price patterns.

*FRAMA (I ) = A (i) * Price (i) + (1 – A(i)) * FRAMA(i-1)*

Where;

*FRAMA (i) — current value of FRAMA;*

*Price (i) — current price;*

*FRAMA(i-1) — previous value of FRAMA;*

*A (i) — a current factor of exponential smoothing.*

The EMA is calculated as:

*A (i) = EXP (-4.6 * (D(i) – 1))*

Where:

*D (i) — current fractal dimension;*

*EXP() — a mathematical function of an exponent.*

The dimensions of the Fractals in a straight line is equal to 1. So, if *D = 1, then A = EXP(-4.6 *(1-1)) = EXP(0) = 1.*

Now the formula looks like

*FRAMA (i) = 1 * Price (i) + (1 — 1) * FRAMA (i—1) = Price (i)*

In a plane the fractal dimensions are equal to 2. By putting this value in the formula:

*A = EXP (-4.6*(2-1)) = EXP (-4.6) = 0.01.*

The smaller values have the same period like 200-period SMA.

Now the formula of fractal dimension is:

*D = (LOG (N1 + N2) – LOG (N3))/LOG (2)*

It is calculated separately as:

*N (Length,i) = (HighestPrice (i) – LowestPrice (i))/Length*

Where:

*HighestPrice (i) — current period’s maximum length*

*LowestPrice (i) — current period’s minimum length;*

*Values N1, N2, and N3 are equal to:*

*N1 (i) = N (Length,i)*

*N2 (i) = N (Length,i + Length)*

*N3(i) = N (2 * Length,i)*

## How to use Fractal Adaptive Moving Average?

The Fractal Adaptive Moving Average indicator tells the average difference between the highest highs and the lowest lows, depending on the period’s length. The length of the period length may vary according to the trader.

The values obtained through the above-mentioned formula takes the shape of FRAMA. The FRAMA points out crucial price changes. If the price moves in a particular direction, then the indicator follows it.

The two lines that represent the FRAMA illustrates buy and sell signals. If the red line crosses the blue line from above, it’s considered a buy signal. Conversely, when the red line crosses below the blue line, it’s considered a sell signal. Traders can choose if they want to enter the markets and place stop-losses near recent highs and lows. This will depend on the individual trading strategy and money management being implemented.

## Fractal Adaptive Moving Average trading strategy

The FRAMA takes advantage of the fact that markets are fractal and dynamically adjusts the lookback period based on this fractal geometry. The actual calculation is very elaborate and complicated. The FRAMA is often used in combination with other signals and analysis techniques. The Fractal Adaptive Moving Average can be applied on any timeframe and trading instruments. Thus, every type of trader can apply FRAMA as part of their trading strategy.

### Fractal Adaptive Moving Average buy strategy

- The red line should cross above the blue line.
- Wait for the price bar to go bullish before entry.
- Place a stop-loss near the recent swing low.
- Exit the trade on high.

### Fractal Adaptive Moving Average sell strategy

- The red line should cross below the blue line.
- Wait for the price bar to go bearish before entry.
- Place a stop-loss near the recent swing high.
- Exit the trade on low.

## Fractal Adaptive Moving Average conclusion

Many new forms of moving averages have been created, but not all of them are easy to calculate. The fractal adaptive moving average is one of those unique moving averages, but it offers great prospects. The fractal adaptive moving average (FRAMA), developed by John Ehlers, is an intelligent and adaptive moving average that takes advantage of the fact that price movements assume the fractal configuration and, as such, dynamically adjusts its lookback period based on this fractal geometry. It follows price closely when there are significant moves while remaining flat if the price ranges.

The Fractal Adaptive Moving Average can be used on your trading platform charts to help filter potential trading signals as part of an overall trading strategy. Although the calculation of the Fractal Adaptive Moving Average is complex, the outcome can help traders. It mentions exact entry and exit points, and can be used to try and follow the direction of the overall trend.

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